You'll have to conduct a name and trademark search to make sure no one else is using the name you want to use (or a very similar name) to market similar products or services. You should also check with your county clerk's office to see whether your proposed name is already on the list of fictitious or assumed business names in your county. If you find that your chosen name (or a very similar one) is registered as a trademark, or is listed on a fictitious or assumed name register, you shouldn't use it.
If you're organizing your business as a corporation, LLC, or limited partnership, you must also make sure your business name isn't the same as that of an existing corporation, LLC, or limited partnership in your state. If a name that is identical or very similar to your proposed business name turns up in your state's database, you'll have to choose another.
Read Make Sure Your Proposed Business Name Is Available for instructions on how to do a thorough name and trademark search.